How to move object around like it's a 3D object
I'm sorry in advance for not expressing this very well.
Here's my image:

I'd like to move/transform the web layer (top layer) in such a way that, the core is pointing away from the viewer. I want to twist the form in a way that it creates a dome over the background.
I know of perspective wrap and puppet wrap, but neither of these tools seem to work. It's usually impossible to create a point exactly where I want it (the center), and even if you can do it, it's impossible to pull away from the viewer like the image is a 3D object.
What tool can I use to create the desired effect, and do I need to do this outside of photoshop? Thing is, it's such a simple manipulation I thought I'd be able to figure it out in Photoshop. Any help? Thank you in advance.

